%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL359-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 01:07:19 PM UTC 2026
% Result : Unsatisfiable 0.23s 0.56s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of clauses : 9 ( 6 unt; 0 nHn; 9 RR)
% Number of literals : 13 ( 0 equ; 5 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL359-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w)))),
file('LCL359-1.p',unknown),
[] ).
cnf(5,axiom,
~ is_a_theorem(implies__dfg(implies__dfg(x__dfg,y__dfg),implies__dfg(implies__dfg(z__dfg,x__dfg),implies__dfg(implies__dfg(y__dfg,u__dfg),implies__dfg(z__dfg,u__dfg))))),
file('LCL359-1.p',unknown),
[] ).
cnf(13,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(implies__dfg(v,w),implies__dfg(u,w))) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.0,1.1')] ).
cnf(17,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,v)),x),implies__dfg(implies__dfg(w,u),x))),
inference(sor,[status(thm)],[13,2]),
[iquote('0:SoR:13.0,2.0')] ).
cnf(35,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,v)),x))
| is_a_theorem(implies__dfg(implies__dfg(w,u),x)) ),
inference(res,[status(thm),theory(equality)],[17,1]),
[iquote('0:Res:17.0,1.1')] ).
cnf(113,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(implies__dfg(x,v),implies__dfg(u,implies__dfg(x,w))))),
inference(sor,[status(thm)],[35,17]),
[iquote('0:SoR:35.0,17.0')] ).
cnf(470,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(w,u),implies__dfg(implies__dfg(v,x),implies__dfg(w,x))))),
inference(sor,[status(thm)],[35,113]),
[iquote('0:SoR:35.0,113.0')] ).
cnf(475,plain,
$false,
inference(unc,[status(thm)],[470,5]),
[iquote('0:UnC:470.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL359-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.03 % Command : run_spass %d %s
% 0.09/0.35 % Computer : n027.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 5 22:40:13 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.23/0.56
% 0.23/0.56 SPASS V 3.9
% 0.23/0.56 SPASS beiseite: Proof found.
% 0.23/0.56 % SZS status Theorem
% 0.23/0.56 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.56 SPASS derived 455 clauses, backtracked 0 clauses, performed 0 splits and kept 274 clauses.
% 0.23/0.56 SPASS allocated 76480 KBytes.
% 0.23/0.56 SPASS spent 0:00:00.19 on the problem.
% 0.23/0.56 0:00:00.06 for the input.
% 0.23/0.56 0:00:00.00 for the FLOTTER CNF translation.
% 0.23/0.56 0:00:00.02 for inferences.
% 0.23/0.56 0:00:00.00 for the backtracking.
% 0.23/0.56 0:00:00.07 for the reduction.
% 0.23/0.56
% 0.23/0.56
% 0.23/0.56 Here is a proof with depth 5, length 9 :
% 0.23/0.56 % SZS output start Refutation
% See solution above
% 0.23/0.56 Formulae used in the proof : condensed_detachment cn_1 prove_cn_08
% 0.23/0.56
%------------------------------------------------------------------------------